Cutting Plexiglass?

I have a problem to solve. I would like to attach my conservatory to the house. I would like for the french doors to open out into the new room.

It looks like the door frame will fit? I just need to make an opening for it.

My problem is, how do I cut the plexiglass? It is in one big piece across the entire bank of windows. I want to cut an opening in the center but I don't want to break it!

Got any ideas?